Geodesic
Inversion formulas for complex Radon transform on projective varieties and boundary value problems for systems of linear PDEs
Informatics and Automation, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 242-256 
Gennadi M. Henkin; Peter L. Polyakov. Inversion formulas for complex Radon transform on projective varieties and boundary value problems for systems of linear PDEs. Informatics and Automation, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 242-256. http://geodesic.mathdoc.fr/item/TRSPY_2012_279_a15/
@article{TRSPY_2012_279_a15,
     author = {Gennadi M. Henkin and Peter L. Polyakov},
     title = {Inversion formulas for complex {Radon} transform on projective varieties and boundary value problems for systems of linear {PDEs}},
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     year = {2012},
     volume = {279},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2012_279_a15/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $G\subset\mathbb C\mathrm P^n$ be a linearly convex compact set with smooth boundary, $D=\mathbb C\mathrm P^n\setminus G$, and let $D^*\subset(\mathbb C\mathrm P^n)^*$ be the dual domain. Then for an algebraic, not necessarily reduced, complete intersection subvariety $V$ of dimension $d$ we construct an explicit inversion formula for the complex Radon transform $R_V\colon H^{d,d-1}(V\cap D)\to H^{1,0}(D^*)$ and explicit formulas for solutions of an appropriate boundary value problem for the corresponding system of differential equations with constant coefficients on $D^*$.

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